Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 2241-2273 |
| Seitenumfang | 33 |
| Fachzeitschrift | Algebra and Number Theory |
| Jahrgang | 7 |
| Ausgabenummer | 9 |
| Publikationsstatus | Veröffentlicht - 2013 |
| Extern publiziert | Ja |
Abstract
We prove new inequalities concerning Brauer's k(B)-conjecture and Olsson's conjecture by generalizing old results. After that, we obtain the invariants for 2-blocks of finite groups with certain bicyclic defect groups. Here, a bicyclic group is a product of two cyclic subgroups. This provides an application for the classification of the corresponding fusion systems in a previous paper. To some extent, this generalizes previously known cases with defect groups of types D2n × C2m, Q2n × C2m and D2n * C2m. As a consequence, we prove Alperin's weight conjecture and other conjectures for several new infinite families of nonnilpotent blocks. We also prove Brauer's k(B)-conjecture and Olsson's conjecture for the 2-blocks of defect at most 5. This completes results from a previous paper. The k(B)-conjecture is also verified for defect groups with a cyclic subgroup of index at most 4. Finally, we consider Olsson's conjecture for certain 3-blocks.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Algebra and Number Theory, Jahrgang 7, Nr. 9, 2013, S. 2241-2273.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Further evidence for conjectures in block theory
AU - Sambale, Benjamin
PY - 2013
Y1 - 2013
N2 - We prove new inequalities concerning Brauer's k(B)-conjecture and Olsson's conjecture by generalizing old results. After that, we obtain the invariants for 2-blocks of finite groups with certain bicyclic defect groups. Here, a bicyclic group is a product of two cyclic subgroups. This provides an application for the classification of the corresponding fusion systems in a previous paper. To some extent, this generalizes previously known cases with defect groups of types D2n × C2m, Q2n × C2m and D2n * C2m. As a consequence, we prove Alperin's weight conjecture and other conjectures for several new infinite families of nonnilpotent blocks. We also prove Brauer's k(B)-conjecture and Olsson's conjecture for the 2-blocks of defect at most 5. This completes results from a previous paper. The k(B)-conjecture is also verified for defect groups with a cyclic subgroup of index at most 4. Finally, we consider Olsson's conjecture for certain 3-blocks.
AB - We prove new inequalities concerning Brauer's k(B)-conjecture and Olsson's conjecture by generalizing old results. After that, we obtain the invariants for 2-blocks of finite groups with certain bicyclic defect groups. Here, a bicyclic group is a product of two cyclic subgroups. This provides an application for the classification of the corresponding fusion systems in a previous paper. To some extent, this generalizes previously known cases with defect groups of types D2n × C2m, Q2n × C2m and D2n * C2m. As a consequence, we prove Alperin's weight conjecture and other conjectures for several new infinite families of nonnilpotent blocks. We also prove Brauer's k(B)-conjecture and Olsson's conjecture for the 2-blocks of defect at most 5. This completes results from a previous paper. The k(B)-conjecture is also verified for defect groups with a cyclic subgroup of index at most 4. Finally, we consider Olsson's conjecture for certain 3-blocks.
KW - 2-blocks
KW - Alperin's weight conjecture
KW - Bicyclic defect groups
KW - Brauer's k.B/-conjecture
UR - http://www.scopus.com/inward/record.url?scp=84892698451&partnerID=8YFLogxK
U2 - 10.2140/ant.2013.7.2241
DO - 10.2140/ant.2013.7.2241
M3 - Article
AN - SCOPUS:84892698451
VL - 7
SP - 2241
EP - 2273
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 9
ER -